The ends of a segment located on one side of a straight line are at a distance of 3 cm and 9 cm from it. At what distance from this straight line is the middle of this segment.
Consider a quadrilateral ABCD.
AB and CD are perpendicular to the same line AD. If two lines are perpendicular to the third line, then these two lines are parallel.
Therefore AB // CD. In the same way, one can prove that AB // CD // MN
Hence the quadrilateral ABCD is a rectangular trapezoid.
MN is its middle line, since M is the middle of BC and MN // AB // CD.
The middle line of the trapezoid is equal to half the sum of the bases.
MN = (AB + CD) / 2 = (3 + 9) / 2 = 6 cm.
Answer. 6 cm.
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